document.write( "Question 921458: Limx->1 $\"%28x%5E8-1%29%2F%28x%5E7-1%29\"$
\n" ); document.write( "(Limit as x approaches 1)
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Algebra.Com's Answer #559001 by KMST(5328) $\"\"$ $\"About$

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There is probably a theorem that tells you what the limit should be, but who wants to memorize theorems?
\n" ); document.write( "We know that
\n" ); document.write( " $\"x%5E8-1=%28x-1%29%28x%5E7%2Bx%5E6%2Bx%5E5%2Bx%5E4%2Bx%5E3%2Bx%5E2%2Bx%2B1%29\"$
\n" ); document.write( "and
\n" ); document.write( " $\"x%5E7-1=%28x-1%29%28x%5E6%2Bx%5E5%2Bx%5E4%2Bx%5E3%2Bx%5E2%2Bx%2B1%29\"$ .
\n" ); document.write( "We can multiply and check, but we get the idea from what we remember.
\n" ); document.write( "We remember that

\n" ); document.write( "from geometric sequences sums,
\n" ); document.write( "or at least we can generalize from remembering from polynomials that
\n" ); document.write( " $\"x%5E2-1=%28x-1%29%28x%2B1%29\"$ and $\"x%5E3-1=%28x-1%29%28x%5E2%2Bx%2B1%29\"$ .
\n" ); document.write( "So, for $\"x%3C%3E1\"$ ,
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,
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